Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

MeganDarling

  • 3 years ago

A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

  • This Question is Closed
  1. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Start off by defining variables

  2. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)

  3. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okey (:

  4. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?

  5. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That they add up to 11 pounds haha

  6. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    good, so x y and z add to 11, which means x+y+z = 11

  7. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's one equation

  8. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so x+y+z=11 :o

  9. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  10. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    But then we have to factor in how much they cost..

  11. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars

  12. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21

  13. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so like, 1.50x+3.00y+1.50=21..

  14. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Haha Okey you already said that x.x my bad

  15. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1.50z* I meant btw haha. I get that indeed.

  16. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    close, you mean to say 1.50x+3.00y+1.50z=21 but you got it

  17. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And don't forget twice the peanuts!

  18. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's your 2nd equation

  19. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    twice the peanuts as what?

  20. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it says, the recipe calls for twice as many peanuts as almonds O.o

  21. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    good, so the equation for that is?

  22. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.

  23. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not quite

  24. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    knew it was wrong x.x

  25. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Amount of peanuts = 2 times (amount of almonds)

  26. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    y = 2 times x or just y = 2x

  27. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh pshh I should have thought of that x.x

  28. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x

  29. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can use them to solve for x, y and z

  30. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'll get you started

  31. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Lol I can't because I'm stupid, But smart people definitely can haha

  32. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x+y+z = 11 x+2x+z = 11 3x+z = 11 --------------------- 1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21

  33. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21

  34. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me

  35. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    where are you lost?

  36. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11

  37. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21

  38. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh okay ! I see now, sorry it's really late and I'm super tired :/

  39. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so you have 3x+z = 11 7.5x + 1.5z = 21 now

  40. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    solve the first equation for z to get this 3x+z = 11 3x+z - 3x = 11 - 3x z = 11 - 3x

  41. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Alrighty

  42. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Since z = 11 - 3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11 - 3x) = 21 Solve for x

  43. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh wait, i made a variable mistake...i switched x and y one sec

  44. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let me fix real quick

  45. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I was thinking that haha x) ..

  46. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    uhh ? your comment disappeared .. :o

  47. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11 - 3y --------------------------- 1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11 - 3y) = 21 Solve that last equation for y

  48. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sry

  49. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Solve 6y + 1.5(11 - 3y) = 21 for y

  50. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    haha it's okay

  51. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Aw man I have to go to bed soon I'm dead tired x.x

  52. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What do you get when you solve that equation for y

  53. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ergh I dunno x.x I'm brain dead

  54. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Then give it a break, get some sleep and you'll tackle it in the morning

  55. MeganDarling
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh no I keep losing connection >.<

  56. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy